What is factor (2x-z)^3+125y^3 ?

The solution to factor (2x-z)^3+125y^3 is (5y+2x-z)((2x-z)^2-5y(2x-z)+25y^2)

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factor (2x-z)^3+125y^3

factor

(2 x - z)^{3} + 125 y^{3}

(5 y + 2 x - z) ((2 x - z)^{2} - 5 y (2 x - z) + 25 y^{2})

Solution steps

(2 x - z)^{3} + 125 y^{3}

Rewrite

(2 x - z)^{3} + 125 y^{3}

(2 x - z)^{3} + (5 y)^{3}

= (2 x - z)^{3} + (5 y)^{3}

Apply Sum of Cubes Formula:

x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})

(2 x - z)^{3} + (5 y)^{3} = ((2 x - z) + 5 y) ((2 x - z)^{2} - 5 (2 x - z) y + 5^{2} y^{2})

= (5 y + (2 x - z)) ((2 x - z)^{2} - 5 y (2 x - z) + 5^{2} y^{2})

Refine

= (2 x + 5 y - z) (25 y^{2} - 5 y (2 x - z) + (2 x - z)^{2})

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(A U B) - C

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What is factor (2x-z)^3+125y^3 ?
The solution to factor (2x-z)^3+125y^3 is (5y+2x-z)((2x-z)^2-5y(2x-z)+25y^2)